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Popular >

derivative of (ln(x)/(e^x))

Solution

\frac{d}{d x} (\frac{ln ( x )}{e ^{x}})

Solution

\frac{1 - x ln ( x )}{e ^{x} x}

Solution steps

\frac{d}{d x} (\frac{ln ( x )}{e ^{x}})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( ln ( x ) ) e ^{x} - \frac{d}{d x} ( e ^{x} ) ln ( x )}{( e ^{x} ) ^{2}}

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (e^{x}) = e^{x}

= \frac{\frac{1}{x} e ^{x} - e ^{x} ln ( x )}{( e ^{x} ) ^{2}}

Simplify

\frac{\frac{1}{x} e ^{x} - e ^{x} ln ( x )}{( e ^{x} ) ^{2}} : \frac{1 - x ln ( x )}{e ^{x} x}

= \frac{1 - x ln ( x )}{e ^{x} x}

Graph

Popular Examples

integral from 0 to 2 of 1/(sqrt(9-x^2))

\int_{0}^{2} \frac{1}{9 - x ^{2}} d x

derivative of f(x)=3x^4 derivative of

f (x) = 3 x^{4}

limit as x approaches 7 of (x^2-4)/(7-x)

x \to 7 lim (\frac{x ^{2} - 4}{7 - x})

integral of arctan(5t)

\int arctan (5 t) d t

limit as x approaches 0 of (x^2+1)/(x^2)

x \to 0 lim (\frac{x ^{2} + 1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the derivative of (ln(x)/(e^x)) ?
The derivative of (ln(x)/(e^x)) is (1-xln(x))/(e^xx)
What is the first derivative of (ln(x)/(e^x)) ?
The first derivative of (ln(x)/(e^x)) is (1-xln(x))/(e^xx)